I don't see the point in responding to every single argument there, especially since a lot of them are very weak and many are variations of the same ideas. But here's my assessment:
1- I think the problem of evil is by far the strongest argument the atheist has to offer. And most arguments in the list are really just variations of it. I differ from most people here in thinking that Brian Davies's and Hart's responses (as I understand them; I haven't read their books, but people have presented their ideas to me, I have read excerpts, did some research, etc., and don't think my opinion would change) are almost entirely useless. I think the defenses and theodicies we find among contemporary analytic philosophers, including "theistic personalists", are 1000x better and even necessary. God is not wholly unlike a virtuous person; if there is to be at least an analogy between God's goodness and ours, we need to assume God has intelligible morally sufficient reasons for allowing so much evil and suffering. And with that in mind:
A) It is always important to approach theism on the basis of the totality of evidence. In other words, we can grant that the problem of evil is really bad and in fact lowers the probability of theism. But that's not the whole story, for we also have positive arguments for theism. And I think the positive case for God's existence is a lot stronger, so as to be compelling and even withstand the attack of PoE and still swamp it out. Evil lowers the probability of theism, but still, the existence of contingent things, order, consciousness, goodness, etc. gives us a much stronger overall case for theism;
B) We can, in any case, weaken the problem of evil. In my opinion, the best response is Alexander Pruss's "blink of an eye" response (google it) combined with a host of theodicies. For all we know, an infinite afterlife can more than make up for, sublimate, etc., any evils we suffer in our finite existence here. And to this we add the Free Will defense; the soul building theodicy; and more;
C) If horrendous evils are still a problem, an explicitly Christian response (like that of Adams in her book on horrendous evils) may be required. The fact that God entered the picture through Jesus Christ, and suffered so much, can be a game changer. Those who suffer horribly in this life can be united in a special way to the suffering Christ God, converting pain into a love and dignity that lasts forever;
D) Animal suffering can still be a specific problem requiring specific responses. We might adopt a few ad hoc ideas (Pruss thinks it plausible that God removes the qualia of pain from animals in some situations), or we can adopt a radical response, such as Trent Dougherty's in his book on animal pain. Dougherty argues that God might transform every animal into a rational, Narnia-esque being in the afterlife and that their sufferings here may therefore be given a value similar to that in soul-building theodicies.
Of course, in any case, there is skeptical theism and we can choose to take a hit and keep moving; while the problem of evil can be a good atheistic argument, we nevertheless have stronger reasons to believe in God. And personally, I find theodicies very plausible - blink of an eye, soul building, free will, the religiously-inspired ones; I even find some plausibility in the radical animal theodicies. I don't think the amount of suffering we see is clearly incompatible with theism, I think it can make a lot of sense that God would choose to create a world like this.
2- Argument from hiddenness I take to be a weaker version of the problem of evil. There can be value in discovery; in being sorta in the dark and even having doubts; in having to dedicate oneself to studying a metaphysical issue such as God's existence; etc;
3- Arguments from materialism I find particularly weak. I'm very convinced that dualism is true and I think it is very strong evidence for theism; there are perfections of immaterial consciousness, intelligence, reason, will, etc., and there must be a source for them. Personhood must come from a foundational Person. And even if materialism were true animal, multiple realizability could allow for intelligence to be material in humans but immaterial in God;
4- Problem of material causation I find quite weak. A theist could be open to biting the bullet with a few caveats, as Rasmussen does in his dialogue with Leon. In any case, I think the idea that matter is a perfection to be very implausible; matter is just a limitation, an act of existence intrinsically limited to spatial location, extension, temporal change, etc., so an immaterial (more perfect) being can create a material (less perfect) being. Moreover the Kalam might refute such an argument;
5- Incoherence arguments I don't take too seriously. I am not convinced of any particular arguments for omni-God being incoherent, I think there are good responses in the literature for all of that. But if a theist is convinced that even a suitably defined omnipotence/omniscience/etc is incoherent, they can bite the bullet and instead adopt Yujin Nagasawa's Maximal God thesis. God just is the Maximal, metaphysically consistent and possible set of Power, Knowledge and Goodness. If a being can't be omniscient, still there can be a maximally knowledgeable being, and ao on.
The rest of the arguments I just find very weak. I don't think any of that even comes close to the cogency and power of theistic arguments; that we need God to explain Being, Consciousness, Order, Value, etc.